Parallel mechanism

ABSTRACT

A parallel mechanism is capable of positioning and orienting an end platform with up to six or more degrees of freedom. In preferred embodiments, the mechanism includes six links having a first and second ends. The first end is connected to an end platform for supporting a tool, while the second end is connected to an actuator capable of translating the second end. A rotational drive mechanism may be provided for rotating an object mounted on the end platform at varying orientations of the end platform independently of movement of the end platform as a whole. The links may be curved in order to avoid interference between adjoining links, thereby permitting an increased range of motion and improved dexterity of the mechanism.

This application is a 371 of PCT/US98/17722 filed Aug. 27, 1998 whichclaims benefit of Prov. No. 60/056,237 filed Aug. 28, 1997.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to multiple degree-of-freedom (DOF)parallel mechanisms which can provide quick and precise manipulativecapabilities.

2. Description of the Related Art

The vast majority of multiple degree-of-freedom mechanisms that are usedin robotic or teleoperator applications are so-called serial mechanisms.A serial mechanism is one in which a plurality of links are connectedtogether in series to form an open chain and are moved with respect toeach other by actuators connected between them to manipulate an objectsupported at the remote end of the chain of links. This type ofmechanical mechanism has the advantages of the ability to access largeworkspaces, and of simplicity of design and geometric analysis. It hasbeen shown that the forward kinematic problem is always directlysolvable for serial mechanisms. The forward kinematic problem is definedas the task of solving for the position and orientation of the remoteend of the mechanism on which a tool is mounted, given the lengths ofall of the links and the angles between adjoining links.

Despite the above mentioned advantages, serial mechanisms are inherentlyplagued with a number of disadvantages. For one, the links at the baseof a serial mechanism must support all of the more remote links of themechanism. As a result, large actuators are required to drive theactuated joints at the base of the mechanism. For precise control, it isadvantageous to have an actuator as close as possible to the tool orother object being driven by the actuator. With a serial mechanism,having an actuator close to the object being driven compromises theoverall performance of the mechanical system, since actuators aretypically heavy electric motors. In the case of a robotic wrist, forexample, the designer must choose between locating the actuators thatdrive the robotic wrist directly at the wrist joints, and locating thewrist actuators towards the base of the robot and using a complex seriesof cables, gears, or other transmission devices to connect the wristactuators to the wrist joints. The former choice allows precise controlof the wrist but also requires that elbow and shoulder actuators locatedcloser to the base support these wrist actuators, resulting in a largeload being applied to the elbow and shoulder actuators. The latterchoice reduces the moving mass which the elbow and shoulder actuators ofthe robot must support, but it also introduces numerous potentialsources of error in the control of the position and/or force of thewrist, including backlash, friction, and wear. Another problem of serialmechanisms occurs when the position of the mechanism remote from asupport structure is determined by sensors, such as encoders, which arelocated at the joints of the mechanism and measure the angles betweenadjoining links. Errors in measurement by the encoders are cumulative,i.e., the error in the calculated position of the remote end of themechanism is a sum of errors of the individual encoders, so it isdifficult to determine the position of the remote end with accuracy.Even when there is no encoder error, calculation of the position of theremote end may be inaccurate due to bending of the links forming theserial mechanism. These problems occur not just with robotic wrists butwith serial mechanisms in general.

Another variety of multiple degree-of-freedom mechanism is referred toas a parallel mechanism. In parallel mechanisms, a plurality ofactuators drive a tool or other object in “parallel”, typically via aplurality of stiff links and joints. The term parallel in this sensemeans that the links share the load being supported by the mechanism,and it does not require that the links be geometrically parallel orimply that they are. Parallel mechanisms are inherently stiffer,quicker, more accurate, and capable of carrying higher loads than serialmechanisms. This is because parallel mechanisms have multiple mechanicaltics between a base support structure and the object being supported sothat the weight of the object is divided among a plurality of members,whereas in serial mechanisms, each link must support the entire weightof the object. A well-known example of a parallel mechanism is theStewart Platform in which a load is supported by a plurality of linkswhich can be adjusted in length by actuators to vary the position andorientation of the load. A parallel mechanism typically has all of itsactuators mounted either on or relatively close to a base supportstructure, so the actuators either do not move or move very littleduring the operation of the mechanism. This minimizes the moving mass ofthe mechanism, making it much quicker than an equivalent serialmechanisms. Furthermore, since the entire load carried by the mechanismis not applied to each actuator as in a serial mechanism but isdistributed among the actuators, the load capacity of the mechanism canbe greatly increased relative to that of a serial mechanism withoutrequiring large capacity (and thus bulky and heavy) actuators. Inaddition, errors in encoders or other sensors for sensing the positionor orientation of the links forming a parallel mechanism are averagedrather than summed as in a serial mechanism, so the position andorientation of a load can be determined with high accuracy. A parallelmechanism is akin to a truss or space frame-type structure in which aload is supported by multiple paths to ground rather than by a singlepath. A mechanism is considered fully parallel if it has no actuatorsconnected in series.

In spite of such advantages, parallel mechanisms have not achievedwidespread acceptance as robotic or teleoperated devices due to a numberof drawbacks. One is that conventional parallel mechanisms have limitedreachable workspaces compared to serial mechanisms, so they are limitedto tasks which do not require large workspaces. This is in part becauseparallel mechanisms have multiple mechanical ties to a fixed supportstructure whereas serial mechanisms have only one, and in part becausethe parallel links of a parallel mechanism can interfere with oneanother in certain positions. In addition, the forward kinematicsproblem for a parallel mechanism can be extremely complexmathematically, and in many cases it is not solvable, often making realtime control of a parallel mechanism difficult or impossible.

Aside from the above problems, both parallel and serial mechanisms ofconventional design tend to suffer from backlash in the components,relatively high friction, a narrow operational bandwidth, and highinertia which make high positional resolution and highly sensitive forcecontrol difficult to achieve.

SUMMARY OF THE INVENTION

The present invention provides a parallel mechanism for robotic orteleoperator (master/slave) applications which can operate with six ormore degrees of freedom and which can overcome many of the disadvantagesof known parallel mechanisms.

According to one form of the present invention, a parallel mechanism formanipulating an object includes a platform for supporting an object tobe manipulated, a plurality of links each having a first end rotatablyconnected to the platform and a second end spaced from the platform withthe platform being kinematically restrained by the links, and aplurality of linear motors each associated with one of the links fortranslating the first end of the corresponding link to move theplatform. The use of linear motors to translate the links enablessmooth, precise control of the movement of the mechanism and/or theforce exerted by the mechanism, making it highly suitable for use in theassembly or manipulation of delicate objects. Linear motors also help togive the mechanism a low inertia, which is highly advantageous from thestandpoint of speed and accuracy of control.

According to another form of the present invention, a parallel mechanismfor manipulating an object includes a platform for supporting an objectto be manipulated, a plurality of links each having a first endrotatably connected to the platform and a second end spaced from theplatform with the platform being kinematically restrained by the links,an actuator associated with each link for translating the first ends ofthe links to move the platform, and a rotatable support member rotatablymounted on the platform for supporting an object to be manipulated. Inpreferred embodiments, the rotatable support member comprises arotatable tool plate mounted on the platform. The support member ispreferably rotated by a drive member which is spaced from the platformand coupled to the support member in a manner enabling the drive memberto rotate the support member with respect to the platform at varyingangles and positions of the platform relative to the drive member. Therotatable support member enables an object supported by it to be rotatedby a greater amount and at a faster speed than is possible by movementof the links alone. Furthermore, the support member can prevent anobject supported by it from rotating while the rotational position ofthe platform is adjusted.

According to yet another form of the present invention, a parallelmechanism includes a plurality of links connected to a platform forsupporting an object to be manipulated with the platform beingkinematically restrained by the links, with at least one of the linksbeing a nonlinear link having a portion not coinciding with a straightline between its first and second ends. Nonlinear links increase therange of movement of the platform before links interfere with eachother, resulting in a larger workspace for the mechanism, as well as theability to employ link geometries giving the mechanism high dexterity.

According to still another form of the present invention, a parallelmechanism includes six links having first and second rotatable joints atits opposite ends, with the first joints connecting the links to aplatform for supporting an object to be manipulated and with theplatform being kinematically restrained by the links. The centers ofrotation of the first joints are spaced at substantially equal angularintervals about a first axis, and the centers of rotation of the secondjoints are spaced at substantially equal angular intervals about asecond axis when the mechanism is in a reference position. Having thejoints equally spaced about the axes results in high dexterity, meaningthat the mechanism can apply roughly the same forces and moments in anydirection and enables the mechanism to be as compact as possible.

A parallel mechanism according to the present invention is capable ofhaving a high mechanical bandwidth, a low inertia, a high dexterity, andlow frictional resistance, all of which combine to enable it to operatewith a high degree of position and force control unattainable byconventional serial or parallel mechanisms.

A parallel mechanism according to the present invention can be used inany application in which an object needs to be manipulated in space withone or more degrees of freedom. A few examples of possible applicationsin various fields are as follows.

Industrial Applications

A parallel mechanism according to the present invention can be used as ageneral purpose manipulator or a robotic arm for manipulating anydesired device in an industrial application, including parts to beassembled, workpieces being processed, manufacturing tools (cuttingtools, welding tools, sensors, painting equipment, etc.), and sensors(cameras, distance sensors, movement sensors, temperature sensors, etc.)for forming images or gathering other information about the workenvironment in which the mechanism is located. When the mechanism isequipped with a rotatable tool plate, the tool plate can be used torotate a workpiece or a tool for various purposes including drilling,screw driving, fastening, milling, deburring, and tightening. Themechanism is capable of being miniaturized as well as being made aslarge as desired, so it can be used in applications ranging from heavyindustrial applications down to microassembly or micromachining.

Medical Applications

The end platform of a parallel mechanism according to the presentinvention can be used to support a medical device, such as a diagnosticdevice or a surgical tool. Because the links and the end platform can bemade extremely small, the mechanism can be used either for surgerythrough a large surgical opening or for endosurgery through a smallsurgical opening or body orifice. Because the end platform is capable ofbeing manipulated with high accuracy and dexterity and can provide forcefeedback to the user, the parallel mechanism is particularly suitablefor use in surgery by remote control. The ability of the mechanism toadjust the position of the end platform with a resolution on the orderof nanometers makes the mechanism highly suitable for medicalapplications requiring precise, fine motions, and particularly formicrosurgery performed with the aid of a microscope, including eyesurgery, ear, nose and throat surgery, neurosurgery, and micro-hand ormicro-orthopedic surgery.

Support Device

Because of its stiffness and ability to dynamically adjust the positionof a load, the parallel mechanism can be used as a general purposesupport. For example, it can be used to support a camera, a surveyinginstrument, or a telescope.

Control Device

A parallel mechanism according to the present invention can be used as amaster control device with up to six or more degrees of freedom in amaster-slave system. Instead of the end platform being used to support aload, the end platform or a handle attached to the end platform can begrasped by a user who manipulates the end platform like a joy stick in adesired manner. The movement of the ends of the links remote from theend platform or changes in the lengths of the links resulting from themovement of the end platform can be sensed to determine the movement ofthe end platform of the master, and commands for controlling the slavemechanism can be generated based on the sensed movement of the master. Aparallel mechanism according to the present invention is particularlysuitable as a master control device when the slave device which is to becontrolled is another parallel mechanism according to the presentinvention.

Construction and Maintenance

A parallel mechanism according to the present invention can be used in amanner similar to a conventional crane or “cherry picker” to supportequipment, materials, or workers.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically illustrates an embodiment of a parallel mechanismaccording to the present invention having fixed-length passive links.

FIG. 2 schematically illustrates another embodiment of a parallelmechanism according to the present invention having variable-lengthactive links.

FIGS. 3-7 schematically illustrate various examples of link geometriesin a parallel mechanism according to the present invention.

FIG. 8 is a more concrete isometric view of an embodiment of a parallelmechanism according to the present invention.

FIG. 9 is an isometric view of an embodiment of FIG. 8 with a base ofthe mechanism removed for clarity.

FIG. 10 is an isometric view of the base and one of the linear actuatorsof the embodiment of FIG. 8.

FIG. 11 is an isometric view of two of the links of the embodiment ofFIG. 8.

FIG. 12 is an enlarged isometric view of the lower joint of one of thelinks of the embodiment of FIG. 8.

FIG. 13 is an exploded isometric view of the end platform of theembodiment of FIG. 8.

FIG. 14 is a vertical cross-sectional view of the end platform of FIG.13.

FIG. 15 is an isometric view showing a rotary actuator of the embodimentof FIG. 8.

FIG. 16 is a block diagram of an example of a control system for theembodiment of FIG. 8.

DESCRIPTION OF PREFERRED EMBODIMENTS

FIG. 1 schematically illustrates an embodiment of a parallel mechanismaccording to the present invention. This embodiment includes an endplatform 10 which can be used to support and manipulate a load 11, suchas a tool, a sensor, a workpiece, or any other member which it isdesired to support and manipulate in space. The end platform 10 is inturn supported by a plurality of links 12, each of which has a first endpivotably connected to the end platform 10 and a second end pivotablyconnected to an actuator 13 which is capable of translating the secondend and exerting a force on the end platform 10 through the link 12. Theactuators 13 are supported atop a suitable support member 14, which maybe a stationary member, such as a rigid base or table, or it may be amovable member, such as a robotic arm. The actuators 13 are controlledby a controller 15 which controls the operation of the actuators 13either autonomously to enable the mechanism to function as an autonomousrobot, or based on an input from a suitable input device, such as a joystick 16. Operation of the actuators 13 to translate the second ends ofthe links 12 changes the position of the first ends of the links 12 tochange the position and/or orientation of the end platform 10 supportedby the links 12. The mechanism is shown in FIG. 1 as being substantiallyvertically oriented with the end platform 10 located above the actuators13, but the mechanism can have any desired orientation with respect tothe vertical permitted by the rigidity of the links 12.

The links 12 are typically rigid members capable of transmitting acompressive load, although if the end platform 10 is always locatedbeneath the actuators 13, the links 12 may be tension members, such asflexible cables, which only support a tensile load. In the mechanismshown in FIG. 1, the links 12 are of the type referred to as passivelinks, meaning that the lengths of the links 12 normally remain constantduring operation of the mechanism (ignoring changes in length due tostresses and temperature), with movement of the end platform 10 beingachieved by translation of both ends of the links 12 rather than by achange in the lengths of the links. However, passive links need not beincapable of changes in length and may include adjusting screws or othermechanisms which enable their lengths to be adjusted. The links 12 mayalso incorporate shock absorbers or other damping devices for reducingvibrations.

FIG. 2 schematically illustrates another embodiment of a mechanismaccording to the present invention. This embodiment is similar to theembodiment of FIG. 1, but the passive links 12 of that embodiment havebeen replaced with what are referred to as active links 17, each ofwhich has an actuator 18 associated with it, by means of which the link17 can be adjusted in length to adjust the position of the end platform10. The expression “associated with” includes both the situation inwhich the actuator 18 forms a part of the link 17 and the situation inwhich the actuator 18 is external to the link 17 but is operativelyconnected to the link 17 in a manner permitting adjustment of the lengthof the link 17. Each active link 17 has a first end pivotably connectedto the end platform 10 and a second end pivotably connected to a supportmember 14, which may be stationary or movable like the support member 14in the embodiment of FIG. 1. The operation of the actuators 18 to adjustthe lengths of the links 17 is controlled by a controller 15 which isconnected to the actuators 18 and which may operate autonomously orbased on an input from a joy stick 16 or other suitable input device.

In the arrangements of both FIGS. 1 and 2, when the links are rigidmembers, the link geometry is such that the end platform 10 iskinematically restrained by the links, meaning that the position ororientation of the end platform 10 can be changed only by moving thesecond ends of the links (in the case of FIG. 1) or by changes in thelengths of the links (in the case of FIG. 2). In other words, simplerotation of the links about their second ends unaccompanied bytranslation of the second ends or changes in the lengths of the linkswill not changes the position or orientation of the end platform.

A parallel mechanism according to the present invention is not limitedto having only active links or only passive links, and two types oflinks can be employed in a single mechanism. Furthermore, an active linkmay have its lower end movably supported, in which case it can functionas a hybrid of an active link and a passive link.

Either an active link or a passive link may extend along a straight linebetween the two ends of the link, or a link may extend along a pathwhich deviates from a straight line between its two ends. As describedbelow, with some link geometries, the range of movement of the linksbefore interference occurs between adjoining links can be significantlyincreased by giving the links a nonlinear shape, such as curved,crank-shaped, V-shaped, etc. For simplicity of structure and control,the links will generally be of the same length as each other, but it isalso possible for the lengths to vary among the links.

A mechanism according to the present invention can have various numbersof links depending upon the number of degrees of freedom with which itis desired to manipulate the end platform. Typically, it will have sixlinks so as to enable the end platform to be controlled with six degreesof freedom, but it may have fewer links if a lesser degree of control isdesired. It is possible to have more than six links, although having alarge number of links will typically increase the complexity of controland possibly reduce the range of movement of the end platform before thelinks interfere with each other.

The links of a parallel mechanism according to the present invention canbe arranged in a wide variety of geometries. Three examples of possiblegeometries which can be employed either with active links or passivelinks are shown in FIGS. 3-7. FIGS. 3, 5, and 7 are isometric views ofthe three different geometries, and FIGS. 4 and 6 are plan views of thegeometries of FIGS. 3 and 5, respectively. Each figure represents areference position of the mechanism with respect to which the upper endsof the links can be translated to change the position or orientation ofan unillustrated end platform supported atop the upper ends of thelinks. The small circles at the ends of the links represent the centersof rotation of joints connecting the ends of the links to other members,such as an end platform, a support base, or an actuator. Each joint isassumed to have a single center of rotation, i.e., all axes of rotationof a given joint are assumed to intersect at a single point. Forsimplicity, each link is shown as a straight line extending between thejoints at its two ends, but a link may instead extend non-linearlybetween the joints. While it will be assumed that the upper ends of thelinks in the figures are connected to the end platform which is to bemanipulated, the end platform could instead be connected to the lowerends of the links.

In the reference position of the geometry shown in FIG. 3, the centersof rotation 21 of the joints at the upper ends of three links 20 arelocated on a first circle 23 having an axis 27, and the centers ofrotation 22 of the joints at the lower ends of these links are locatedon a second circle 24 which has an axis 28 and which is coaxial with butspaced in the axial direction from the first circle 23. The centers ofrotation 21 of the joints at the upper ends of three more links 20 arelocated on a third circle 25 coplanar and coaxial with the first circle23, and the centers of rotation 22 of the joints at the lower ends ofthese links 20 are located on a fourth circle 26 coplanar and coaxialwith the second circle 24. In this figure, the second circle 24 islarger than the first circle 23 and the fourth circle 26 is larger thanthe third circle 25 so that the links 20 are sloped inwards with respectto the axes 27 and 28 of the circles from circles 24 and 26 to circles23 and 25, but the diameters of the circles can be selected so that thelinks are sloped in the opposite direction, i.e., the second circle 24can be smaller than the first circle 23 and the fourth circle 26 can besmaller than the third circle 25. Alternatively, the diameters of thevarious circles can be selected such that some of the links 20 aresloped inwardly and the other links are sloped outwardly from circles 24and 26 to circles 23 and 25. The centers of rotation 21 of the sixjoints on the first and third circles 23 and 25 are substantiallyequally spaced around the common axis 27 of these circles, i.e., theyare located at angular intervals of approximately 60 degrees, and thecenters of rotation 22 of the six joints on the second and fourthcircles 24 and 26 are likewise substantially equally spaced around thecommon axis 28 of these circles. As shown in FIG. 4, which is a planview of the mechanism illustrated in FIG. 3, the angular position of thecenter of rotation 21 of the upper joint of each link 20 with respect tothe angular position of the center of rotation 22 of the lower joint ofthe same link 20 is such that when the mechanism is viewed along thealigned axes 27, 28 of the four circles 23-26, adjoining links 20 appearto intersect each other, although they do not actually intersect whenthe mechanism is in its reference position. Therefore, in FIG. 3, halfof the links 20 have been drawn as broken lines to indicate that thereis no intersection between the links 20. In the reference position, ifthe centers of rotation 22 of the joints at the lower ends of the links20 are located on circles 24 and 26 at angles of approximately 0, 60,120, 180, 240, and 300 degrees around the aligned axes 27, 28 of thecircles (taking the position of the center of rotation 22 of anarbitrary one of the joints as 0 degrees), then the centers of rotation21 of the joints at the upper ends of the same links 20 are located oncircles 23 and 25 at approximately 60, 0, 180, 120, 300, and 240degrees, respectively. The arrows passing through the centers ofrotation of the lower joints of the links 20 in FIG. 3 illustrateexamples of paths of movement for these joints when the links 20 arepassive links rotatably connected to unillustrated actuators at theirlower joints.

FIG. 5 is an isometric view of a link geometry in which, in theillustrated reference position, each of six links 30 of equal length hasa joint at its upper end having a center of rotation 31 located on afirst circle 33 and a joint at its lower end having a center of rotation32 located on a second circle 34 coaxial with but spaced axially fromthe first circle 33, and FIG. 6 is a plan view of the geometry of FIG.5. The centers of rotation 31 of the joints at the upper ends of thelinks 30 are substantially equally spaced, i.e., located at intervals ofapproximately 60 degrees around the axis 35 of the first circle 31, andthe centers of rotation 32 of the joints at the lower ends aresubstantially equally spaced around the axis 36 of the second circle 34.This geometry is one which results by combining the first and thirdcircles 23 and 25 in FIG. 3 with each other and by combining the secondand fourth circles 24 and 26 of FIG. 3 with each other. When themechanism is viewed along the aligned axes 35, 36 of the circles 33 and34, as shown in FIG. 6, adjoining links 30 appear to intersect eachother. As with the arrangement shown in FIGS. 3 and 4, in the referenceposition, the centers of rotation 32 of the joints at the lower ends ofthe links 30 are located at angles of approximately 0, 60, 120, 180,240, and 300 degrees around the aligned axes 35 and 36 of the circles 33and 34 (taking the position of the center of rotation 32 of an arbitraryone of the joints as 0 degrees), while the centers of rotation 31 of thejoints at the upper ends of the same links 30 are located atapproximately 60, 0, 180, 120, 300, and 240 degrees, respectively. Inthe reference position shown in FIG. 5, adjoining links 30 will actuallyintersect with each other if each link 30 extends along a straight lineconnecting the centers of rotation 31 and 32 of the joints at its upperand lower ends. Therefore, for the link geometry shown in FIG. 5. Atleast one-half of the links 30 (every other link) will have a shapedeviating from a straight line to prevent interference between links 30when the mechanism is in the reference position as well as to increasethe range of movement in which no interference takes place.

The link geometry shown in FIG. 7 is that of a typical Stewart Platformin which the centers of rotation 41, 42 of the joints at the upper andlower ends, respectively, of six links 40 of equal length are grouped inthree pairs on a first circle 43 and on a second circle 44 coaxial withand axially spaced from the first circle 43 when the mechanism is in areference position. With this geometry, the links 40 do not appear tointersect each other when the mechanism is viewed along the aligned axesof the first and second circles 43 and 44.

Numerous other geometries are possible by modifying the abovegeometries. For example, the various upper and lower circles can havedifferent axes; the centers of rotation of the joints at the upper endsof the links may lie on a single circle while the centers of rotation ofthe joints at the lower ends lie on multiple circles or vice versa; thecenters of rotation of the joints at the ends of the links need not beevenly spaced around the respective circles; the centers of rotation ofthe joints at the upper or lower ends of the links need not lie in asingle plane; and the links may be non-uniform in length.

Of the various geometries which can be employed, geometries in which thelinks appear to cross each other when the mechanism is viewed along thealigned axes of the upper and lower circles are preferred because, forcircles of a given radius and separation, such geometries permit thelinks to be sloped at a greater angle to the axes of the circles than ifthe links do not appear to cross. As the angle of a link with respect tothe axes of the circles increases, the greater is the force which can beexerted on an end platform by the upper end of the link in a directionperpendicular to the axes. With a typical Stewart platform geometry suchas that shown in FIG. 7, the links 40 are at a fairly small angle withrespect to the axes of the first and second circles 43 and 44, with theresult that the force which can be exerted by the links in a directionparallel to the axes is much greater than the force which can be exertedby the links in a direction normal to the axes. With geometries such asthose shown in FIGS. 3 through 6 in which the links appear to cross eachother, the force which can be exerted in a direction normal to the axesis closer in magnitude to the force which can be exerted parallel to theaxes, so a mechanism having one of these geometries has a greaterdexterity.

Having the centers of rotation of the joints spaced substantiallyequally around an axis when the mechanism is in its reference positionis advantageous because it permits a large work space by reducinginterference between links. Even spacing of the centers of rotation ofthe joints also increases the stiffness of the mechanism as well asresults in the most compact base for the mechanism when the actuatorsare placed as close to each other as possible.

Having the centers of rotation of all the upper joints on a singlecircle and having the centers of rotation of all the lower joints onanother circle typically permits a large range of motion and results ina more even distribution of loads on the links, particularly when atorque is applied to the end platform.

As stated above, many of the link geometries which can be employed inthe present invention may utilize either active or passive links.However, passive links frequently have a number of advantages overactive links. Passive links can generally be smaller in diameter thanactive links, so a greater range of movement is possible beforeinterference between adjoining links occurs. In addition, becausepassive links are much simpler in structure than active links, it iseasier to miniaturize a mechanism employing passive links. Furthermore,it is easier to make passive links in a non-linear or other desiredshape than to do so for the active links. Also, since a passive linktypically has no moving parts, it can be designed to have a highstiffness more readily than an active link. In addition, since theactuators for passive links will generally be further from the endplatform than the actuators for active links, it is easier to connectelectrical wiring, hydraulic lines, or other members to the actuatorsfor passive links than for active links. A particularly importantadvantage of passive links over active links is that the moving mass ofa parallel mechanism with passive links can be much less than that of aparallel mechanism of the same size with active links. With an activelink, the actuator is disposed between the two ends of the link, so theentire actuator undergoes movement every time the link is changed inlength. In contrast, with a passive link, the actuator is outside of thelink, and generally only a portion of the actuator undergoes movement asthe link moves. As a result, the inertia of the parallel mechanism as awhole is much lower, enabling more rapid changes in direction ofmovement. A lower inertia also increases safety, permits more accuratecontrol of force and position, and results in a higher mechanicalbandwidth.

When the links are active links, the actuators will typically act alonga linear path coinciding with a line connecting the two ends of thecorresponding link. In the case of passive links, the actuators can acton the lower ends of the links in any direction which will produce adesired movement of the upper ends of the links. For simplicity, eachactuator will typically act along a linear path parallel to a commonaxis (such as the axis of one of the lower circles in FIGS. 3-7), butthe paths of movement of the actuators need not be parallel to eachother. Linear actuators which act along a linear path are particularlysuitable, but it is also possible to use non-linear actuators. A widevariety of actuators can be employed, such as linear electric motors,rotary motors connected to motion converting mechanisms (such asball-bearing screws or racks and pinions) for converting rotary tolinear motion, and hydraulic or pneumatic cylinders. When the endplatform only needs to assume a small number of positions, an actuatorhaving only a small number of discrete states, such as a solenoid, canbe used, but when it is desired to manipulate the end platform with manydegrees of freedom, such as six degrees of freedom, the actuatorspreferably permit substantially continuous position control. Amongvarious types of actuators, linear electric motors are particularlysuitable, especially for applications in which precise control of theend platform is desired.

In the past, parallel mechanisms have been powered either by hydraulicor pneumatic pistons connected to the links, or by rotary motorsconnected to a motion converting mechanism for converting the rotationalmovement of the motors into linear movement for driving the links.Linear electric motors have not been used as link actuators in parallelmechanisms. However, linear electric motors have a number of importantyet hitherto unrecognized advantages over conventional actuators whenemployed in parallel mechanisms.

One advantage is that linear motors produce a linear output force, sothey can be used to directly drive either an active link or a passivelink of a parallel mechanism without the need for ball bearing screws orother motion converting mechanisms (which produce backlash, increasedinertia, and increased friction, all of which are detrimental to precisecontrol of a mechanism) to be disposed between the linear motors and thelinks. Thus, a parallel mechanism with linear motors as actuators can becontrolled with extremely high precision.

Another advantage of using linear motors as actuators in a parallelmechanism is that the moving mass of a linear motor is essentiallyindependent of the range of movement of the moving portion of the motor.In contrast, for most other types of actuators, including hydrauliccylinders or motors connected to ball bearing screws, an actuator with along range of movement will tend to have a greater moving massundergoing rotation and/or translation than an actuator with a shortrange of movement. Therefore, a parallel mechanism employing linearmotors as actuators can have a long range of movement while still havinga low moving mass and low inertia.

Still another advantage of linear motors is that they have very lowfriction, which is highly advantageous from the standpoint of achievingaccurate force control and/or position control. This low frictionresults in linear motors being backdrivable, i.e., they can be driven byan external force exerted in the direction opposite to the direction ofthe force exerted by the motor.

The ends of each link are equipped with joints which enable each end topivot with multiple degrees of freedom with respect to a member to whichthe link is connected (such as an end platform, a base, or an actuator)during the operation of the mechanism. Various types of rotatable jointscan be used for this purpose, such as universal joints (Hooke's joints,etc.) or spherical joints (ball and socket joints, etc.). Preferably thejoint at one end of each link enables the link to pivot with threedegrees of freedom relative to the member to which the one end isconnected, while the joint at the other end of the link enables the linkto pivot with at least two degrees of freedom relative to the member towhich the other end is connected. For example, the joint at one end canhave three rotational degrees of freedom while the joint at the otherend has two rotational degrees of freedom, or both joints can permitthree rotational degrees of freedom. Calculation of the kinematics ofthe mechanism is simpler if each joint has a single center of rotation,i.e., if all of axes of rotation of the joint intersect at a singlepoint, but the joints may also be of a type which does not have a singlecenter of rotation.

FIGS. 8-16 are more concrete illustrations of an embodiment of aparallel mechanism of the type shown in FIG. 1 employing passive linksdriven by linear actuators. FIG. 8 is an isometric view of theembodiment, and FIG. 9 is an isometric view of the same embodiment witha support base of the mechanism removed for clarity. The mechanismincludes an end platform 100 for supporting a load, six curved links 110supporting the end platform 100, and a linear actuator 140 comprising alinear motor 141 associated with each link 110. The mechanism alsoincludes a base 170 for supporting the actuators 140 and for maintaininga desired spacing between them. The upper end of each link 110 ispivotably connected to the end platform 100 by an upper universal joint120 having two axes of rotation, and the lower end of each link 110 ispivotably connected to one of the actuators 140 by another universaljoint 130 having three axes of rotation. The links 110 are of equallength and identical shape and are arranged in the geometry shown inFIG. 5, with the centers of rotation of the upper joints 120 equallyspaced around a first circle and with the centers of rotation of each ofthe lower joints 130 equally spaced around a second circle coaxial withand axially spaced from the first circle when the mechanism is in areference position.

The end platform 100 in this embodiment is generally disk-shaped, but itcan have any shape suited to the equipment which it needs to support orthe shape of the space in which it is to be manipulated, such aspolygonal or a combination of polygonal and curved shapes. While theillustrated end platform 100 has an upper surface which is substantiallyflat, it may be convex, concave, stepped, or otherwise deviate from aplanar shape. The end platform 100 can be used to support a variety oftools, sensors, or other objects, depending upon the task which it is toperform, and its shape or other structural features can be selected inaccordance with the nature of the object which is to be supported.

FIG. 10 is a detailed view of one of the linear actuators 140 and thecorresponding link 110 which is driven by it. Each actuator 140 includesa permanent magnet DC linear motor 141, such as those manufactured byTrilogy Systems of Webster. Texas, although many other varieties andbrands of linear motors can be employed, such as AC vector drive linearmotors. Of the various types of permanent magnet DC linear motors whichexist, moving-coil motors are preferable to moving-magnet ormoving-armature types because moving-coil motors provide a higherforce-to-inertia ratio, although these other types may also be employed.The illustrated linear motors 141 are moving-coil motors including amagnet track 142 comprising a plurality of permanent magnets disposed inseries, and a coil unit 143 comprising a set of coils wrapped on anonmagnetic support bar made of aluminum, for example, and movablydisposed in a slot of the magnet track 142 for linear movement in thelengthwise direction of the magnet track 142. In the present embodiment,the magnet track 142 is mounted on the base 170 of the mechanism. Themagnet track 142 may have any desired length appropriate for the desiredrange of movement of the end platform 100. The coil unit 143 may besupported for linear movement solely by the magnet track 142, butdepending upon the load which is to be applied to the coil unit 143 andthe sturdiness of the linear motor 141, it may be desirable to supportthe coil unit 143 for movement by a linear guide exterior to the motor141 in order to reduce the mechanical load on the motor and reduce playbetween the magnet track 142 and the coil unit 143. Therefore, in thepresent embodiment, the coil unit 143 is supported by a conventionallinear guide 144, such as a ball slide having a stationary block 145secured to the base 170 and a sliding bar 146 secured to the coil unit143 and slidably supported by the block 145 for linear movement. A ballslide is particularly suitable as the linear guide 144 because it canhave an extremely low coefficient of friction. Examples of suitable ballslides are those available from THK Co. Ltd. of Japan, which have acoefficient of friction on the order of 0.000125. As a result, thestarting friction of the linear guide 144 is so low that the linearmotor 141 (and therefore the lower joint 130 of the corresponding link110) can be moved in extremely fine increments, resulting in itsposition being controllable with a high degree of precision. The upperend of the sliding bar 146 of the linear guide 144 is rigidly secured tothe lower universal joint 130 of one of the links 110. The linear motors141 in the present embodiment are controlled by digital sine wavecommutation, although other types of motor control, such as pulse widthmodulation control, can instead be performed.

The current passing through the coil unit 143 may produce an increase inthe temperature of the sliding bar 146 of the linear guide 144,resulting in its thermal expansion. To prevent the thermal expansionfrom decreasing tolerances and increasing the friction of the linearguide 144, the mechanism may be equipped with an unillustratedtemperature controller which senses the temperature of the sliding bar146 and the block 145 and heats the block 145 of the linear guide 144with a heating coil or similar member associated with the block 145 sothat the temperature of the block 145 is made to match that of thesliding bar 146, thereby preventing temperature gradients and uneventhermal expansion.

FIG. 11 illustrates two adjoining links 110 of the embodiment of FIG. 8.Each link 110 is curved away from a straight line connecting the centersof rotation of the two joints 120, 130 at its ends to increase the rangeof movement of the links 110 without interference between adjoininglinks 110. One of the links 110 is bowed outwardly with respect to thecentral axis of the mechanism and the other link 110 is bowed inwardly,but the direction in which the links 110 are curved and the amount ofcurvature are not restricted to those shown in the illustratedarrangements and can be selected based on factors such as the desiredstrength of the links 110 and geometric constraints on the particulardesign. Up to a certain degree, the greater the eccentricity of thelinks (equal to the maximum deviation of the centerline of a link from astraight line connecting the two ends of the link), the greater theamount of movement of the links which is possible before adjoining linksinterfere with each other, although if the eccentricity of a link is toogreat, the link may interfere with other parts of the mechanism or withobjects on the exterior of the mechanism. On the other hand, the bendingmoment which is applied to a link under a given load will generallyincrease as the eccentricity increases, possibly requiring an increasein the cross-sectional dimensions and the unit weight of the link inorder for the link to withstand the increased bending moment. Thus, asuitable eccentricity of the links will depend upon the parameters (suchas the permissible amount of movement without interference or thedesired weight of the mechanism) which the designer wishes to optimize.An example of a suitable eccentricity is on the order of 10%.

When the mechanism is to be used for high precision manipulation, suchas in surgery, in high precision machining, or in the assembly of finemanufactured parts, the links 110 are preferably as stiff as possible togive the mechanism a high resonant frequency and a high mechanicalbandwidth. At the same time, the links 110 are preferably as light aspossible to give the mechanism a very low inertia. Thus, for suchapplications, materials having a high ratio of stiffness to density areparticularly suitable for use in forming the links 110. One example ofsuch a material is AlBeMet, which is a trademark for a powder metalmaterial including powders of aluminum and beryllium. AlBeMet isavailable from Brush Wellman of Elmore, Ohio. AlBeMet has a density onthe order of 0.08 lb/in³ and a Young's modulus on the order of 30×10⁶psi, (giving it an excellent stiffness to density ratio. It is alsonon-brittle, isotropic, and machinable. Other examples of materialswhich are suitable when a high stiffness to density ratio is desired forthe links 110 are carbon fiber composites. However, the links 110 are byno means restricted to being formed of these materials and can beselected based on the physical properties desired for the particularapplication.

FIG. 12 shows in detail the universal joint 130 connecting the lower endof one of the links 110 to a moving portion of one of the actuators 140.It includes an upper yoke 131 rotatably connected by one or morebearings 134 (such as a pair of preloaded bearings) to the lower end ofthe link 110, and a lower yoke 132 secured to the moving portion of theactuator 140. The two yokes 131 and 132 are each rotatably connected toan end of a cross piece 133 having two orthogonal axes about which theyokes can pivot. Each lower universal joint 130 therefore has three axesof rotation. For simplicity of calculating the kinematics of themechanism, the two axes of rotation of the yokes 131 and 132 about thecross piece 133 preferably intersect each other, and more preferably allthree axes of rotation intersect at a single point, as in the presentembodiment. However, it is also possible for the axes to benon-coincident.

The joint 120 connecting the upper end of the link 110 to the endplatform 100 is similar in structure to the joint 130 for the lower endand includes an upper yoke 121 and a lower yoke 122, each rotatablyconnected to a cross piece 123 having two orthogonal axes of rotation.For simplicity of calculating the kinematics of the mechanism, the twoaxes of rotation are preferably intersecting. The lower yoke 122 isrigidly secured to the upper end of the link 110, while the upper yoke121 is rigidly secured to the end platform 100. As a result, the upperjoint 120 provides only two rotational degrees of freedom. However, byrotatably connecting one of the yokes 121, 122 to either the link 110 orthe end platform 100, the upper joint 120 may provide three rotationaldegrees of freedom. In order to increase the stiffness of the mechanism,the upper yokes 121 may be integrally formed with the end platform 100if desired.

The kinematics of the mechanism are simpler to compute if the axis ofrotation of the link 110 with respect to the upper yoke 131 of the lowerjoint 130 coincides with a straight line connecting the center ofrotation of the upper joint 120 and the center of rotation of the lowerjoint 130, but this axis may be non-coincident with this line.

In order to calculate the position of the end platform 100 at any time,it is desirable to know the position of the lower end of each link 110.The position of the lower end of the link 110 can be sensed directly,but it is generally easier to sense the position of a member connectedto the link, such as the moving portion of the linear actuator 140associated with the link 110. The position of the actuator 140 can besensed by a wide variety of conventional sensing mechanisms which sensethe movement or the position mechanically, magnetically, optically, orin another manner, including potentiometers, linearly variablydifferential transformers, optical encoders, and Hall effect sensors.When fine control of the position of the end platform 100 is desired, aholographic interferometric linear encoder is particularly suitable foruse as a position sensor because it can sense absolute position with aresolution of as fine as 10 nanometers. Such absolute linear positionsensors 150 are employed in the present embodiment. Each position sensor150, which is manufactured by MicroE Inc. of Natick, Mass., includes aposition scale 151 secured to a moving portion of the actuator 140, suchas the sliding bar 146 of the linear guide 144, and a position reader152 mounted on a stationary portion of the mechanism, such as the base170, with the position scale 151 movably disposed in a slot of theposition reader 152. The position reader 152 generates an electricaloutput signal which indicates the location of the position scale 151 andwhich is provided to an electronic controller.

Three of the lower universal joints 130 are equipped with two rotationalposition sensors 160 for sensing the rotational position of acorresponding link 110 about two orthogonal axes. Like the linearposition sensors 150 for the linear actuators 140, the rotationalposition sensors 160 may have any structure and operate based upon anyphysical principle. Holographic interferometric encoders similar tothose used for the linear position sensors 150 for the linear actuators140 are particularly suitable when a high resolution of position sensingis desired. The illustrated sensors 160 are holographic interferometricencoders manufactured by MicroE Inc. and include an arcuate positionscale 161 and a position reader 162 having a slot in which the positionscale 161 is movably disposed. The position reader 162 provides theelectronic controller with an output signal indicative of the absoluterotational position of the position scale 161 and thus indicative of theangle of the link 110 about one of the axis of rotation of the lowerjoint 130. Each position reader 162 is secured to one of the yokes 131,132 of the universal joint 130, while the position scale 161 is securedto one leg of the cross piece 133 on which the two yokes 131 and 132 ofthe universal joint 130 are rotatably mounted so that each positionscale 161 is capable of rotational movement relative to thecorresponding position reader 162.

By suitably controlling the movement of the links 110, it is possible torotate the end platform 100 about an axis passing through andperpendicular to the plane of the end platform 100 while otherwisemaintaining the orientation of the end platform 100 constant. However,the amount of rotation of the end platform 100 which is achievable inthis manner before adjoining links 110 interfere with each other toprevent further rotation is limited, and there may be situations inwhich is it desired to rotate the tool or other object mounted on theend platform 100 by a greater number of degrees than is possible bytranslation of the links 110. To permit a greater amount of rotation,the end platform 100 may be equipped with a rotatable support membersuch as a rotatable tool plate 105 on which an object can be mounted andwhich can be continuously rotated with respect to the end platform 100to provide any desired degree of rotation of the object. A drivemechanism for rotating the tool plate 105 can be mounted on the endplatform 100 itself, but in order to minimize the weight of structuresmounted on the end platform 100 so as to improve the responsiveness andcontrollability of the mechanism, in the present embodiment, the toolplate 105 is rotated by a motor 180 of any suitable type (such as abrushless, slotless DC motor) mounted on the base 170 and connected tothe tool plate 105 in a manner which permits the motor 180 to transmitdrive torque to the tool plate 105 at any orientation and location ofthe end platform 100 with respect to the motor 180. As shown in FIG. 15,two universal joints 181 and 182 drivingly connected to each other by ashaft 184 are disposed between the motor 180 and the tool plate 105. Theupper yoke of the upper universal joint 181 is secured to a shaft 183which is drivingly connected to the tool plate 105, while the lower yokeof the lower universal joint 182 is connected to the rotor of the motor180 in a manner which permits the lower universal joint 182 and therotor to undergo relative movement in the axial direction of the motor180 while preventing them from rotating with respect to each other sothat torque can be transmitted by the motor 180 to the lower universaljoint 182. In the present embodiment, the lower universal joint 182 isconnected to the motor 180 by a ball spline, but any other suitable typeof connecting member for transmitting torque while permitting axialmovement can be employed. The ball spline includes a spline shaft 185secured to the lower yoke of the lower universal joint 182 and anunillustrated ball nut which is slidably mounted on the spline shaft 185and secured to the rotor of the motor 180 so as to rotate with it. Therotor of the motor 180 is hollow, so the spline shaft 185 can passthrough the center of the rotor as the spline shaft 185 slides up anddown with respect to the ball nut. Examples of suitable ball splines arethose available from THK Co. Ltd. As the end platform 100 is movedtowards and away from the base 170 by operation of the linear actuators140, the lower universal joint 182 can undergo axial movement relativeto the motor 180 so that the motor 180 can rotate the tool plate 105 atvarying distances of the tool plate 105 from the base 170. Furthermore,the universal joints 181 and 182 enable the tool plate 105 to be rotatedby the motor 180 in any orientation of the end platform 100 with respectto the base 170. By suitably controlling the motor 180, the tool plate105 can be rotated at speeds ranging from a few rpm or less when thetool plate 105 is used for slow positioning of an object up to thousandsof rpm when the tool plate 105 is used for machining or other tasksinvolving high speed rotation.

FIGS. 13 and 14 are respectively an exploded isometric view and avertical cross-sectional view showing the structure of the end platform100 and the tool plate 105 which is rotatably supported by the endplatform 100. For compactness, the tool plate 105 may be recessed in acavity 101 of the end platform 100 to reduce its overall height. Forexample, the upper surface of the tool plate 105 may be substantiallyflush with the upper surface of the end platform 100. The tool plate 105may be located anywhere on the end platform 100 and may be rotatablysupported by the end platform 100 in any suitable manner. In the presentembodiment, its axis of rotation coincides with the axis of the circleon which the centers of rotation of the upper joints 120 of the links110 are located, and the tool plate 105 is rotatably supported by a pairof cross roller bearings 106 which may be preloaded to reduce play.

The mechanism may be equipped with one or more force sensors for sensingexternal forces acting on the end platform 100 so that the motions ofthe end platform 100 can be controlled in accordance with the sensedforces. Force sensors can be disposed in a variety of locations on themechanism, with the end platform 100 being a particularly suitablelocation since there the sensors can directly sense the applied forces.In the present embodiment, a six degree of freedom force-torquetransducer 108 is mounted on the end platform 100 in the cavity 101beneath the tool plate 105. The lower surface of the transducer 108 issecured to the bottom of the cavity 101, and the upper surface of thetransducer 108 is secured to a support plate 107 on which the two crossroller bearings 106 are mounted. The transducer 108 can sense axialforce along three orthogonal axes and moments about these three axes andgenerate corresponding output signals, which are provided to theelectronic controller. The transducer 108 which may be of any desiredtype. An example of a suitable force-torque transducer is asemiconductor strain gauge-type available from ATI Industrial Automationof Garner, N.C. The transducer 108 has a central bore through which theshaft 183 for connecting the tool plate 105 to the upper universal joint181 can pass.

The tool plate 105 may be equipped with suitable structure, such asscrew holes, brackets, or a chuck, by means of which a tool or otherobject can be secured to the tool plate 105. The portion of the endplatform 100 surrounding the tool plate 105 may be equipped with similarstructure for supporting various objects.

If desired, the tool plate 105 may be omitted, and a tool or otherobject which is to be rotated by the motor 180 may be connected directlyto the shafting extending from the motor 180. In this case, all or aportion of the object can be disposed in the cavity 101 in the endplatform 100, with only a portion of the object extending above the topsurface of end platform 100, thereby decreasing the overall height ofthe mechanism. If the shafts connecting the tool plate 105 and the motor180 are hollow, electrical wiring, fluid conduits, cables, fibers, orother members can conveniently pass through the shafts between the toolplate 105 and the base 170.

An example of a situation in which a rotatable tool plate 105 isparticularly useful is when a parallel mechanism according to thepresent invention is used for machining. A workpiece to be machined canbe mounted atop the tool plate 105 and rotated with respect to a toolsupported by another member, or a tool can be mounted on the tool plate105 and rotated with respect to a workpiece supported by another member.Machining of highly complex shapes can be performed if a workpiece issupported atop one parallel mechanism according to the present inventionwhile a cutting tool is supported atop the tool plate 105 of anotherparallel mechanism according to the present invention.

Although the tool plate 105 is capable of being rotated independently ofthe end platform 100, there may be circumstances when it is desired torotate the end platform 100 and the tool plate 105 as a unit, since thelinks 110 may be capable of exerting a higher torque on the end platform100 than the motor 180 for the tool plate 105. Therefore, the tool plate105 may be equipped with a locking mechanism, such as an electric brake,which can releasably lock the tool plate 105 to the end platform 100when desired.

The tool plate 105 can be used to rotate a tool or other object in spaceabout its axis, but it can also be used to restrain an object againstrotation when the end platform 100 is being rotated in space. As statedabove, the links 110 are capable of rotating the end platform 100 aboutan axis normal to the end platform 100, but after a certain amount ofrotation, adjoining links 110 will interfere with each other, preventingfurther rotation. When the end platform 100 is equipped with a toolplate 105, after the end platform 100 has been rotated in a firstdirection by the links 110 to the point where adjoining links interfere,the motor 180, in its off state, can be used to maintain the toolstationary while the end platform 100 is rotated backwards in a seconddirection by the links 110 to “untwist” the links 110 from each other sothat they no longer interfere. When the end platform 100 has beenrotated backwards by a desired amount, the tool plate 105 can then belocked to the end platform 100, and the end platform 100 and the toolplate 105 can again be rotated as a unit in the first direction byoperation of the links 110 to rotate the object.

One of the tool plate 105 and the end platform 100 can also be used tosupport an object while the other of the two applies a torque to theobject or to another object engaged with the first object. For example,a nut could be grasped by a tool on the tool plate 105, a bolt could begrasped by another tool on the end platform 100, and the tool plate 105could then be rotated with respect to the end platform 100 to screw thenut onto the bolt. Using the tool plate 105 and the end platform 100 inconjunction with each other in this manner to apply a torque to one ormore objects is convenient in an environment, such as in outer space orunderwater, in which it may be impossible to immobilize the base 170which supports the actuators 140 against rotational movement.

A parallel mechanism according to the present invention will typicallybe equipped with a control unit, such as an electronic controller, fortranslating instructions from an input device into suitable commands forthe linear motors. FIG. 16 illustrates an example of a control systemwhich can be employed in the present invention. It includes anelectronic controller 190 of any suitable type, such as a generalpurpose computer or a special purpose computer with one or more digitalsignal processors. The controller 190 receives input signals from thelinear position sensors 150 for the linear motors 141, the rotationalposition sensors 160 for the lower joints 130 of the links 110, theforce-torque transducer 108 for the tool plate 105, and any othersensors for sensing some operating parameter of the mechanism, such as acamera for forming an image of the end platform 100 or the work space inwhich the end platform 100 is operating. The controller 190 alsoreceives input signals from one or more suitable input devices by meansof which an operator can input the desired movement of the end platform100. Some examples of possible input devices are a joy stick 191, akeyboard 192, a tape memory 193 or other data storage device whichstores instructions for the movement of the end platform 100, a footpedal, a mouse, a digitizer, a computer glove, or a voice operatedcontroller. Based on the input from the input devices 191-193 and thesignals from the position sensors 150 and 160 and the force/torquetransducer 108, the controller 190 calculates or otherwise determines inreal time the position of the end platform 100 and the motion of theindividual links 110 required to move the end platform 100 in thedesired manner. The controller 190 then provides suitable controlsignals to a motor driver 194 which amplifies the control signals usinglinear transconductance amplifiers, for example, and drives theappropriate linear motors 141 or the motor 180 for rotating the toolplate 105 to achieve the desired movement of the end platform 100.Linear transconductance amplifiers reduce force-torque ripple comparedto pulse-width modulation amplifiers when used with digital sine wavecommutation, but any suitable type of amplifier may be employed.

The controller 190 can control the mechanism in a variety of manners,depending upon the requirements of the task which is to be performed bythe mechanism. For example, the controller 190 may perform positioncontrol, force control, or a combination of position and force control(hybrid position/force control) of the mechanism. Examples of these andother suitable control methods capable of use in the present inventionand algorithms for their implementation are well known in the field ofrobotics and described in detail in published literature.

When the axes of the linear actuators 140 are parallel to each other andit is desired to move the end platform 100 along a straight lineparallel to the axes, it is not necessary to know the position of theend platform 100 with respect to the base 170 in order to control themovement of the end platform 100, since the desired linear movement ofthe end platform 100 can be achieved by advancing or retracting themoving portions of all the linear actuators 140 by the same amount.However, if it is desired to move the end platform 100 in any otherdirection, or if the axes of the actuators 140 are not parallel to eachother, it is generally necessary to know the position of the endplatform 100 with respect to the base 170 in order to calculate theamount of movement of the actuators 140 required to move the endplatform 100 in the desired direction. The position of the end platform100 relative to the base 170 can be determined in a variety of ways. Oneway is to calculate the positions of the upper ends of the links 110relative to the base 170 supporting the lower ends of the links 110based on some combination of the lengths of one or more of the links110, the positions of the lower ends of one or more of the links 110,the angular orientations of one or more of the links 110 with respect tothe base 170, and the angular orientations of one or more of the links110 with respect to the end platform 100. For passive links, the lengthsof the links will usually be constant and so will be known in advance.For active links, the length of each link can be calculated with respectto an initial length as the link is shortened or elongated by operationof the actuator forming part of the link. When the lower ends of thelinks are movable, the positions of the lower ends can be senseddirectly or can be determined by sensing the translation of the linearactuator associated with the lower end of each link with respect to areference position. The angular orientation of the links 110 relative tothe base 170 or the end platform 100 can be sensed by installingrotational position sensors on the joints at the lower or upper ends ofone or more of the links 110. It is preferable to have any rotationalposition sensors installed on the lower joints 130 rather than on theupper joints 120 in order to reduce the moment of inertia of themechanism measured from the base 170 so as to increase theresponsiveness of the mechanism as well as to reduce the length ofelectrical wiring required for connecting the rotational positionsensors to a controller. As described above, the embodiment of FIG. 8employs six rotational position sensors 160, with two of the sensors 160mounted on the lower joint 130 of each of three of the links 110. If theaxis of rotation of each of these three links 110 in the correspondingbearing(s) 134 coincides with the center of rotation of the cross piece133 of the lower joint 130 to which the link 110 is connected, theangles sensed by the two rotational position sensors 160 on the lowerjoint 130 define the position of the center of rotation of the upperjoint 120 of the link 110 relative to the position of the center ofrotation of the lower joint 130. Since the positions of the centers ofrotation of the lower joints 130 for these links 110 relative to thebase 170 are known from the output signals from the corresponding linearposition sensors 150, then the positions of the centers of rotation ofthe lower joints 130 and the angles sensed by the rotational positionsensors 160 on the three joints 130 together determine the positionsrelative to the base 170 of the centers of rotation of the upper joints120 for these links 110. The locations of the centers of rotation of thethree upper joints 120 define the location of the end platform 100. Ifthe axis of rotation of one of the links 110 relative to the upper yoke131 of the lower joint 130 does not coincide with the center of rotationof the cross piece 133 of the lower joint 130 to which it is connected,an additional rotational position sensor 160 can be installed on each ofthe three lower joints 130 to sense the rotation of the correspondinglink 110 in the corresponding bearing 134.

The position of the end platform 100 can also be determined using fourrotational position sensors (two rotational position sensors 160 likethose shown in FIG. 8 mounted on two of the lower joints 130 rather thanon three of the joints 130). Given the positions of the centers ofrotation of the two lower joints 130 on which the rotational positionsensors 160 are mounted, the angles sensed by the four rotationalposition sensors enable the positions of the centers of rotation of thetwo corresponding upper joints 120 of the links 110 to be determined.The center of rotation of a third one of the upper joints 120 lies on acircle of known radius containing the centers of rotation of the twoupper joints 120 for which the positions are known. The distance of thecenter of rotation of the third upper joint 120 lies on a sphere ofknown radius centered at the center of rotation of the lower joint 130of the corresponding link 110, the radius of the sphere being determinedby the length of the corresponding link 110. The position of the centerof rotation of the third joint can be determined by calculating the twopoints of intersection of the circle with the sphere. It can be readilydetermined from the geometry of the mechanism which of the two possibleintersections points is the actual location of the center of rotation ofthe third upper joint 120. Once the positions of the centers of rotationof the three upper joints 120 are determined, the position of the endplatform 100 is known.

Yet another method of determining the position of the end platform 100is to employ five rotational position sensors installed on a single link110. Namely, three rotational position sensors 160 can sense rotation ofthe link 110 about the three axes of rotation of the lower joint 130 ofthe link 110 while two more rotational position sensors 160 can sensethe rotation of the upper end of the link 110 with respect to the endplatform 100 about the two axes of rotation of the upper joint 120.Given the location of the center of rotation of the lower joint 130 ofthe link as determined by the linear position sensor 150 for thecorresponding linear actuator 140, the angle sensed by the fiverotational position sensors 160 enable the position of the end platform100 to be determined.

Some of the information obtained by the various sensors may beunnecessary or redundant for the calculation of the forward kinematics.For example, in the arrangement of FIG. 8, the position of the lowerends of the three links 110 not equipped with rotational positionsensors 160 is not necessary for the calculation of the position of theend platform 100. Therefore, linear position sensors 150 for theactuators 140 for these links 110 are unnecessary for the purpose ofsolving the forward kinematics. However, it may still be desirable toequip these actuators 140 with linear position sensors 150 for controlpurposes, i.e., to enable each of the actuators 140 to translate thecorresponding link 110 by a desired amount.

Another way to determine the position of the end platform 100 is tocalculate incremental movements of the end platform 100 starting from aknown reference position based on incremental movements of the lowerends of the links 110, as determined by the linear position sensors 150for the linear actuators 140. The incremental movements of the endplatform 100 can then be summed to give an approximate position of theend platform 100. Since this method does not employ rotational positionsensors 160 on any of the joints of the mechanism, it enables areduction in the weight of the mechanism.

Algorithms which can be used in the present invention to solve theforward kinematics are well known in the art and are readily derivedfrom basic geometric principles. A detailed discussion of methods ofsolving for the forward kinematics of a parallel link mechanism withactive links can be found in the paper “Optimal Sensor Placement forForward Kinematics Evaluation of a 6-DOF Parallel Link Manipulator” byStoughton and Arai (Proceedings of IEEE/RSJ International Workshop onIntelligent Robots and Systems, IROS '91, Volume 2), and the methodsdisclosed in that paper may also be employed with the present invention,either with active or passive links. A description of the forwardkinematics as well as the inverse kinematics of a six-link parallelmechanism according to the present invention is also found in theAppendix. The inverse kinematic problem is the reverse of the forwardkinematic problem and involves solving for the positions of the lowerjoints 130 of the links 110 of a parallel mechanism given the positionand orientation of the end platform 100 of the mechanism.

If the current location and orientation of the end platform 100 areknown from the forward kinematics, the movement of the lower joints 130by the linear actuators 140 from their current positions required tomove the end platform 100 from its current location and orientation to anew location and/or orientation can be found by determining, based onthe inverse kinematics, the displacement of the lower joints 130 from areference position corresponding to the new location and/or orientation,and subtracting the calculated new displacements from the currentdisplacements for the same joints 130.

A parallel mechanism according to the present invention is very suitablefor use as a master device in a master-slave teleoperated system becauseit can provide the operator with accurate feedback of the forces beingapplied to the slave device. The slave device can be any desiredmechanism, such as another parallel mechanism according to the presentinvention. An example of master-slave operation in which both the masterand the slave are parallel mechanisms similar to the ones shown in FIG.8 is as follows. The two mechanisms may be of the same or differentsizes from each other, with the master being either larger or smallerthan the slave. Making the master smaller than the slave is useful whenit is desired for the slave to magnify the movements of the master, suchas when the slave is being used to move objects large distances. On theother hand, making the master larger than the slave is useful when it isdesired for the slave to perform microscopic motions which are too finefor an operator to perform by hand. For example, in microassembly,manual movement of the end platform of the master on the order ofmillimeters by the operator can be scaled down to movement of the slaveon the order of micrometers. However, scaling (either magnifying ordecreasing) the motions of the slave relative to those of the master canalso be performed when the master and the slave are the same size.Controlling the slave so as to follow the motions of the master iseasier if the master and the slave are geometrically similar, althoughgeometric similarity is not required for master-slave operation. Themaster typically will not be equipped with a tool plate, but it may beequipped with a handle or other member which can be grasped by theoperator when manipulating the master. When the operator manipulates theend platform of the master to produce a translation or rotation of theend platform, one or more of the lower joints of the links of the masterwill undergo translation, and the linear position sensor associated witheach joint will sense the new positions of the lower joints. Signalsindicative of the new positions will be input to a controller, and thelinear actuator associated with each of the corresponding joints of theslave will be controlled by the controller to move the correspondingjoint of the slave in the same direction that the corresponding joint ofthe master was moved but by an amount scaled by the relative sizes ofthe master and the slave or other scale factor and adjusted inaccordance with any dissimilarities in the geometries of the master andthe slave so that the end platform of the slave will emulate themovement of the end platform of the master. If the force-torquetransducer on the slave does not sense any forces or torques, the forcesexerted by the linear actuators of the master will be such as tomaintain the end platform of the master stationary in any position inwhich it has been left by the operator, so as the operator manipulatesthe end platform, he will feet only the frictional resistance tomovement of the master. However, if a force or torque is exerted on theslave, these forces or torques are converted to an equivalent set offorces exerted by the slave actuators on the lower joints of the linksusing the kinematic equations found in the Appendix, for example. Theseforces are then scaled as desired, and the controller controls theactuators of the master to apply these scaled forces on the lower jointsof the master. In this way, the human operator feels the forcesencountered by the slave.

If the slave device is a device having very little friction, such as aparallel mechanism according to the present invention, force feedbackcan be applied to the master device in the following manner withoutusing the force/torque transducer. The controller drives the actuatorson the master so as to decrease any error between the positions of thelower joints on the master and the positions of the corresponding lowerjoints of the slave. For example, in proportional control of the masterand slave, the force exerted on one of the lower joints of the master bythe corresponding actuator is the sum of a predetermined value dependentupon the weight of the end platform of the master and a valueproportional to the error between the position of the lower joint of themaster and the position of the corresponding lower joint of the slave,while the force exerted on one of the lower joints of the slave by thecorresponding actuator is the sum of a predetermined value dependentupon the unloaded weight of the end platform of the slave and a valueproportional to the error between the position of the lower joint of theslave and the position of the corresponding lower joint of the master.When the slave is able to move freely without obstacles and its endplatform is unloaded, the positions of the master and slave correspondvery closely, and the operator feels only the frictional forces inmoving the devices, which can be made very small when the master andslave arc mechanisms according to the present invention. However, whenthe slave picks up an object, the weight of the object creates adifference between the positions of the lower joints of the master andthe slave. Due to the difference in positions, the controller increasesthe forces exerted by the actuators of the slave, enabling the actuatorsto support the object, but at the same time, the controller increasesthe forces exerted by the actuators of the master by an amountproportional to the difference in positions and therefore proportionalto the weight of the object, thereby enabling the operator of the masterto sense the weight of the object. Depending upon the method of controlwhich is employed, the actuators of the master can continue to exert aforce proportional to the weight of the object on the hand of theoperator, or the forces exerted by the actuators of the master can begradually returned to their initial values so that the operator sensesthe weight of the object only when it is first picked up. Similarly, ifthe slave encounters constraints within its environment (such as whenthe slave contacts an immovable object), the constraint forces createsmall differences in the positions of the joints of the slave and thecorresponding joints of the master, so the controller increases theforces exerted by the actuators of the master, whereby the operatorfeels the constraint forces encountered by the slave.

What is claimed is:
 1. A parallel mechanism for manipulating an objectin space comprising: a platform for supporting an object to bemanipulated; a plurality of links each having a first end movablyconnected to the platform and a second end spaced from the platform withthe platform being kinematically restrained by the links; a plurality offirst rotatable joints each rotatably connecting the first end of one ofthe links to the platform and a plurality of second rotatable jointseach connected to the second end of one of the links, each of the firstjoints having a center of rotation located on a first circle with afirst axis and each of the second joints having a center of rotation,the mechanism having a reference position in which the center ofrotation of each of the second joints is located on a second circlecoaxial with and spaced from the first circle, a line connecting thecenters of rotation of the first and second joints of each link crossinga line connecting the centers of rotation of the first and second jointsof another of the links when the mechanism is in the reference positionand viewed along the first axis; a plurality of linear motors eachassociated with one of the links and having a movable portion capable oftranslating the first end of one of the links to move the platform; arotatable support member rotatably supported by the platform; and adrive member for rotating the rotatable support member spaced from theplatform and drivingly connected to the rotatable support member.
 2. Aparallel mechanism as claimed in claim 1 wherein each of the linearmotors is rotatably connected to the second end of one of the links. 3.A parallel mechanism as claimed in claim 2 wherein the movable portionsof the linear motors are movable parallel to a common axis.
 4. Aparallel mechanism as claimed in claim 2 wherein each of the linearmotors is a moving coil linear motor.
 5. A parallel mechanism as claimedin claim 3 including a plurality of linear guides each supporting themovable portion of one of the linear motors for movement parallel to thecommon axis.
 6. A parallel mechanism as claimed in claim 5 wherein eachlinear guide movably supports a coil of one of the linear motors.
 7. Aparallel mechanism as claimed in claim 1 wherein the first end of eachlink is rotatably connected to the platform.
 8. A parallel mechanism asclaimed in claim 1 including a base supporting the second ends of thelinks, the drive member being mounted on the base.
 9. A parallelmechanism as claimed in claim 1 wherein the drive member is connected tothe rotatable support member in a manner enabling the drive member torotate the rotatable support member at varying angles and positions ofthe platform relative to the drive member.
 10. A parallel mechanism asclaimed in claim 1 wherein the rotatable support member has an axis ofrotation which is fixed with respect to the platform.
 11. A parallelmechanism as claimed in claim 10 wherein the rotatable support membercomprises a support plate for supporting an object rotatably mounted onthe platform.
 12. A parallel mechanism as claimed in claim 1 wherein thedrive member comprises a rotary actuator, the mechanism including adrive shaft for transmitting torque from the rotary actuator to therotatable support member and capable of translating with respect to therotary actuator in an axial direction of the drive shaft as the driveshaft is rotating.
 13. A parallel mechanism as claimed in claim 12including a ball spline connected between the drive shaft and the rotaryactuator.
 14. A parallel mechanism as claimed in claim 9 including auniversal joint connected between the drive member and the rotatablesupport member to enable an angle between the drive member and therotatable support member to vary.
 15. A parallel mechanism as claimed inclaim 1 further including a plurality of sensors each associated withone of the linear motors for generating a signal indicative of movementof the movable portion of the linear motor.
 16. A parallel mechanism asclaimed in claim 15 further including a slave mechanism controlled bythe parallel mechanism.
 17. A parallel mechanism for manipulating anobject in space comprising: a platform for supporting an object to bemanipulated; a plurality of links each having a first end rotatablyconnected to the platform and a second end spaced from the platform, theplatform being kinematically restrained by the links, at least one ofthe links being a nonlinear link having a portion not coinciding with astraight line between the first and second ends of the link; a pluralityof linear motors each associated with one of the links for translatingthe first ends of the links to move the platform; a rotatable supportmember rotatably supported by the platform; and a drive member forrotating the rotatable support member spaced from the platform anddrivingly connected to the rotatable support member.
 18. A parallelmechanism as claimed in claim 17 wherein each of the links is anonlinear link.
 19. A parallel mechanism as claimed in claim 17including six links, at least three of which are nonlinear links.
 20. Aparallel mechanism as claimed in claim 17 wherein the nonlinear link hasa curved region between its first and second ends.
 21. A parallelmechanism as claimed in claim 17 including a plurality of firstrotatable joints each rotatably connecting the first end of one of thelinks to the platform and a plurality of second rotatable joints eachconnected to the second end of one of the links, each of the first andsecond joints having a center of rotation where two axes of rotation ofthe joint intersect, the mechanism having a reference position in whichthe centers of rotation of the first joints lie in a first plane, thecenters of rotation of the second joints lie in a second plane parallelto the first plane, and for each link, a line connecting the centers ofrotation of the first and second joints of the link intersects a lineconnecting the centers of rotation of the first and second joints ofanother of the links, none of the links intersecting each other in thereference position.
 22. A parallel mechanism as claimed in claim 21wherein each link does not contact any of the other links when themechanism is in the reference position.
 23. A parallel mechanism formanipulating an object in space comprising: first through sixth linkseach having a first end and a second end; a platform kinematicallyrestrained by the links for supporting an object to be manipulated; aplurality of first rotatable joints each rotatably connecting the firstend of one of the links to the platform and a plurality of secondrotatable joints each connected to the second end of one of the links,each of the first and second joints having a center of rotation wheretwo axes of rotation of the joint intersect; and an actuator associatedwith each link for translating the first ends of the links to move theplatform, the centers of rotation of the first joints being spaced atsubstantially equal angular intervals about a first axis, and thecenters of rotation of the second joints being spaced at substantiallyequal angular intervals about a second axis wherein the mechanism has areference position in which the centers of rotation of the first jointslie in a first plane and the centers of rotation of the second jointslie in a second plane parallel to the first plane and the centers ofrotation of the first joints are located on two concentric and coplanarcircles.
 24. A parallel mechanism as claimed in claim 23 wherein thecenters of rotation of the first joints lie on a first circle and thecenters of rotation of the second joints lie on a second circle coaxialwith and axially spaced from the first circle when the mechanism is inthe reference position.
 25. A parallel mechanism as claimed in claim 23wherein the centers of rotation of the second joints are located on twoconcentric and coplanar circles when the mechanism is in the referenceposition.
 26. A parallel mechanism as claimed in claim 23 wherein whenthe mechanism is in the reference position, the first and second axesare coincident, the centers of rotation of the first joints of the firstthrough sixth links are located at angles of approximately 0, 60, 120,180, 240, and 300 degrees, respectively, with respect to the axes, andthe centers of rotation of the second joints of the first through sixthlinks are located at angles of approximately 60, 0, 180, 120, 300, and240 degrees, respectively, with respect to the axes when the mechanismis viewed along the axes, taking a location of an arbitrary one of thefirst joints as 0 degrees.
 27. A parallel mechanism for manipulating anobject in space comprising: first through sixth links each having afirst end and a second end; a platform kinematically restrained by thelinks for supporting an object to be manipulated; a plurality of firstrotatable joints each rotatably connecting the first end of one of thelinks to the platform and a plurality of second rotatable joints eachconnected to the second end of one of the links, each of the first andsecond joints having a center of rotation where two axes of rotation ofthe joint intersect; and an actuator associated with each link fortranslating the first ends of the links to move the platform, thecenters of rotation of the first joints being spaced at substantiallyequal angular intervals about a first axis, and the centers of rotationof the second joints being spaced at substantially equal angularintervals about a second axis, wherein the mechanism has a referenceposition in which the centers of rotation of the first joints lie in afirst plane and the centers of rotation of the second joints lie in asecond plane parallel to the first plane and the centers of rotation ofthe second joints are located on two concentric and coplanar circleswhen the mechanism is in the reference position.
 28. A parallelmechanism as claimed in claim 27 wherein the centers of rotation of thefirst joints lie on a first circle and the centers of rotation of thesecond joints lie on a second circle coaxial with and axially spacedfrom the first circle when the mechanism is in the reference position.29. A parallel mechanism as claimed in claim 27 wherein when themechanism is in the reference position, the first and second axes arecoincident, the centers of rotation of the first joints of the firstthrough sixth links are located at angles of approximately 0, 60, 120,180, 240, and 300 degrees, respectively, with respect to the axes, andthe centers of rotation of the second joints of the first through sixthlinks are located at angles of approximately 60, 0, 180, 120, 300, and240 degrees, respectively, with respect to the axes when the mechanismis viewed along the axes, taking a location of an arbitrary one of thefirst joints as 0 degrees.